Available online at www.sciencedirect.com
Energy Procedia 18 (2012) 715 – 723
Fuzzy control adaptive of a matrix converter for harmonic
compensation caused by nonlinear loads
A. Boukadouma, T. Bahib, S. Oudinac, Y. souf a, S. Lekhchineb
a
Department of Electrical Engineering, University Tebessa, Algeria
b
Department of Electrical Engineering, University of Annaba, Algeria
c
Department of Electrical Engineering, University of Skikda, Algeria
Abstract
Since discovered, electrical energy represents one of the most decisive fields in any technological
development achieved by man. However, with the expansion of industrial process requiring not only a lot
of power but also clean electric power, the distribution systems require effectively and efficiently control
strategy. One of the greatest physical phenomena that affects on the quality of electric energy is the
harmonics caused by nonlinear loads connected to the grid, which are generally converters based on power
electronics components. Indeed, these are the main cause of the deterioration of energy quality.
This work presents a topology of harmonic compensation based on a three-phase matrix converter with a
fuzzy controller adaptive. The principal adjustment estimates the output currents in order to calculate the
optimal rate of modulation. Fuzzy controller adaptive was used to not only improve the control strategy of
the converter, but also to improve the quality of energy in accordance with international standards.
To evaluate the effectiveness of the work, we conducted tests of numerical simulations on our model based
on fuzzy control. The results of simulations will be presented and interpreted.
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Keywords- Matrix converter, Adaptive fuzzy control, Harmonic, nonlinear load, THD
* A. Boukadoum Tel.: 00 213-778-581-479-fax: 00 213 388-416-253.
E-mail address: azizboukadoum@yahoo.fr.
1876-6102 © 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of The TerraGreen Society.
Open access under CC BY-NC-ND license. doi:10.1016/j.egypro.2012.05.087
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A. Boukadoum et al. / Energy Procedia 18 (2012) 715 – 723
1. Introduction
The development of new systems called active filters based on semiconductors power are so advanced
solutions for the most appropriate harmonics remediation in the production and distribution of electrical
networks. Their response is instantaneous and adapts automatically to change the disturbances introduced
by nonlinear loads [1]. The number of the elements that constitute these filters, as well as the complexity of
their control, to discover a new type converter called the matrix converter (MC).
This converter has a very important role; it provides direct conversion (AC / AC) without using an
intermediate continuous circuit, and it gives a good quality waveform in the electrical output an adaptive
fuzzy controller's (AFC) for voltage rate. The power grid provides a sinusoidal voltage at the connection
point, whatever the current drawn by the nonlinear load, and disturbances imposed by the source, the
compensation of harmonic disturbances based on a static compensator matrix has adaptive fuzzy controller
was proposed in this new technique.
The objective of this study is to replace conventional active filters by matrix converter topology which
ensures the conversion and filtering of energy at the same time.
Fig.1. Schema of Principe
2. Topology and modeling of matrix converter
The development of MC has started with the work of Venturini and Alesina [2][3], they have presented the
power circuit of the converter as a matrix [ 3*3]. The MC has been proposed by Guygyi Pelly [4]. It
converts a three-phase to three-phase network with another frequency and amplitude variable. It is able to
connect each input phase to each output phase through four segments and nine switches commutated, see
Fig.2. it consists of power circuit and control circuit, his function is ensure the transition adjustment of
electrical power from the source to the receiver [5] [6][7]. The input filter is generally needed to smooth
the input currents, minimized harmonics and to ensure overall system stability [8][9].
Fig.2.Topology of matrix converter
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A. Boukadoum et al. / Energy Procedia 18 (2012) 715 – 723
The input voltage of matrix converter is given by:
v AN (t )
vi (t )
vim cos( i t )
2
)
vim cos( i t
3
4
)
vim cos( i t
3
v BN (t )
vCN (t )
(1)
The input line current amplitude iim and phase
i A (t )
ii (t )
iim cos( i t
2
iim cos( i t
3
4
iim cos( i t
3
iB (t )
iC (t )
i
i , with
the input voltage are defined by:
)
i
)
i
)
(2)
The MC will be designed and controlled for desired output voltage and output currents are determined
respectively by following equations:
vaN (t )
v j (t )
vom cos( o t )
2
)
vaN (t ) vom cos( o t
3
4
vcN (t ) vom cos( o t
)
3
ia ( t )
i j (t )
ib (t )
ic (t )
iom cos(
t
2
iom cos( o t
3
4
iom cos( o t
3
o
o
(3)
)
o
)
o
)
(4)
The switches Sij are characterized a connection function Sij (t) defined by the following equations [8] :
S ij (t )
With
0 if S ij open
1 if S ij closed
i = A, B, C and
(5)
j = a, b, c
We define the generation function mij (t ) of the switches S ij as the average value of the connection
function S ij (t ) intermittently over a period of switching T p :
T
mij (t )
And,
1
S ij (t )dt
Tp 0
with 0
mij (t ) 1
(6)
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A. Boukadoum et al. / Energy Procedia 18 (2012) 715 – 723
m Aa (t ) m Ba (t ) m Ca (t ) 1
m Ab (t ) m Bb (t ) m Cb (t ) 1
m Ac (t ) m Bc (t ) m Cc (t ) 1
(7)
All the generation functions form a matrix called modulation matrix M (t) as:
m Aa (t )
m Ab (t )
m Ac (t )
M (t )
m Ba (t )
m Bb (t )
m Bc (t )
m Ca (t )
m Cb (t )
m Cc (t )
(8)
The conversion matrix of MC connects the electrical as follows:
v j (t )
ii (t )
M (t ) vi (t )
M (t )
T
(9)
i j (t )
Where, M (t ) and
(10)
T
M (t ) are modulation matrix and its transposed.
Initial approach of Venturini method obtain a ratio of maximum voltage, necessary to added a third
harmonic frequency of the input and output voltage indicates at the following equations[7][8] [9]:
v aN ( t )
qv im (cos(
o
v bN ( t )
qv im (cos(
o
t
v cN ( t )
qv im (cos(
o
t
t)
2
3
4
3
1
1
cos( 3 o t )
cos( 3 i t ))
6
2 3
1
1
cos( 3 o t )
cos( 3 i t ))
)
6
2 3
1
1
cos( 3 o t )
cos( 3 i t ))
)
6
2 3
(11)
The modulation rate (q) is the ratio between the maximum amplitude of the output voltage ( v jm ) and the
maximum amplitude of the input voltage ( v im ).
q
v jm
vim
with
0
q
0.86
(12)
The modulations function according to the optimal amplitude in expression of Venturini is:
2viv
1
m ij ( t )
1
1
3
1
2
v
2viv j
2
v im
2viv
v 2 im
j
im
j
4q
sin(
3. 3
4q
sin( i t
3. 3
4q
sin( i t
3 3
i
t ) sin( 3
i
t)
2
) sin( 3
3
4
) sin( 3
3
The switching time were calculated according to equation:
tij (t )
i
i
t)
(13)
t)
mij (t )
Tp
(14)
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A. Boukadoum et al. / Energy Procedia 18 (2012) 715 – 723
3. Control of matrix converter
The carrier signal is tooth an equation defined by:
1
t
Tp
u p (t )
0
t
Tp
(15)
PWM used to divide the period Tp into three intervals [7][9][10]. It’s defined with equations (14) and (15).
The controls switches Sij of MC are obtained using a simple logic binary:
G Aj
X j
G Bj
X
j
et Y
j
G Cj
X
j
et Y
j
(16)
So, the algorithm control switches for one output phase as given in Fig. 3:
Fig .3. PWM control technique of matrix converter
4. Modeling of linear and nonlinear load
The relation currents of a three-phase rectifier bridge as given by:
i1 ( t )
i1 ( t )
u da ( t )
Lc d
1
i2 ( t )
i2 ( t )
u eb ( t )
Rc dt
Rc
i3 ( t )
i3 ( t )
u fc ( t )
(17)
The relation currents of the linear load as given by:
iN ' b
iN ' c
v N ' a max
R
)
L
R (L )
v N ' a max
R
2
cos( t ar tan( )
)
2
2
L
3
R (L )
v N ' a max
R
4
cos( t ar tan( )
)
2
2
L
3
R (L )
iN ' a
2
2
cos( t ar tan(
(18)
So, the output currents of the MC as given:
ia (t )
iN ' a (t ) i1 (t )
ib (t ) iN 'b (t ) i2 (t )
ic (t ) iN ' a (t ) i3 (t )
(19)
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5. Fuzzy control adaptive of a matrix converter
Measurements the output currents of the linear load using a fuzzy controller adaptive as given Fig. 4.
de
dt
FLC
(t )
e
iref
q
PI
Ccontroller
i
Measure
Matrix
converter
Linear
Load
Fig .4. Principal of adaptive fuzzy controller
The measurement output current of linear load as given by:
i
2
2
2
2
(iN ' a (t ) iN 'b (t ) iN ' c (t ))
3
(20)
And, its reference as given in Fig.5.
Fig .5. Reference currents
The reference of the linear load currents is determined by used the Fig. 5.
2 2
(i N 'aref (t ) i 2 N 'bref (t ) i 2 N 'cref (t ))
3
iref
(21)
The instantaneous error e(t) can be calculated by subtracting the value of the currents and its reference
e
iref
i
(22)
The derivative of the error can be calculated by this equation:
de
dt
d
(iref
dt
i)
(23)
The inputs of fuzzy controller FLC are the error (e) and its derivative (de/dt), where the output of FLC is
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A. Boukadoum et al. / Energy Procedia 18 (2012) 715 – 723
the value (t ) : The normalization of the action proportional Kp and the integral Ki destined for the
adaptation of PI[8][11].
The parameters of the fuzzy control adaptive are calculated by:
k'p
'
ki
(t ) K p
(24)
(t ) K i
The output of adaptive controller achieves the desired value ‘’q ‘’ for control the MC.
The following table shows the fuzzy sets of input and output variables:
Table 1 Rules of inference
de
e
NB
NM
NS
ZE
PS
PM
PB
NB
NM
NS
ZE
PS
NB
NB
NM
MN
NS
NS
ZE
NB
NM
NM
NS
NS
ZE
PS
MN
MN
NS
NS
ZE
PS
PS
MN
NS
NS
ZE
PS
PS
MP
NS
NS
ZE
PS
PS
PM
PM
PM
NS
ZE
PS
PS
PM
PM
PB
PB
ZE
PS
PS
PM
PM
PB
PB
6. Simulation results
To evaluate the effectiveness of the work we realized the tests of numerical simulations on the structure
chosen for four different cases of harmonics disturbances.
6.1. Source feeds the linear load (RL) through the MC with AFC
Fig.6. Input voltage source and spectral harmonics analysis
Fig.7. Load linear current and specter harmonics
l i
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6.2. Disturbed Source feeds the linear load (RL) through the MC with AFC
Fig.8. Disturbed input voltage source and spectral harmonics
Fig.9. Load linear current and specter harmonics
6.3. Source feeds the linear load (RL) and nonlinear load (Rectifier Bridge) through the MC with AFC
Fig.10. Nonlinear load currents and spectral analysis
Fig.11. Load linear current and specter harmonics
6.4. Disturbed Source feeds the linear load (RL) and non-linear load through the MC with AFC
Fig.12. input voltage source disturbed
Fig.13. Nonlinear load currents
Fig.14. Load linear current and specter harmonics
A. Boukadoum et al. / Energy Procedia 18 (2012) 715 – 723
The simulation results obtained in all cases clearly show that linear load currents are preserved with the use
of the matrix converter having a fuzzy adaptive controller. The load currents are still sinusoidal whatever
harmonic disturbances affecting the system at the source ( 5th and 7th harmonics) or the nonlinear load ( the
three phase rectifier bridge). In Addition, the spectral analysis of harmonics show clearly the decrease of
these currents THD compared to the spectral analysis of the harmonics generated by the source and the
non-linear load.
7. Conclusion
To evaluate the effectiveness of the results obtained different cases of harmonic disturbances were used.
The results clearly show that linear load currents are preserved with the use of a matrix converter having a
fuzzy adaptive controller. The currents are maintained sinusoidal whatever harmonic disturbances are
affecting the system.
The development of matrix converters with adaptive fuzzy controller not only can improve the control
strategy of the converter, but can also be seen as a useful method that has the ability to protect the output
currents (of the linear load) from of harmonic disturbances that affects them. The simulation results
obtained in this study confirm that the analysis of harmonic currents (THD) of load protection through the
use of this type of adjustment and control of the converter, are significantly reduced.
8. System parameters
Input voltage phase to neuter RMS V=220 V, frequency f =50Hz
Input filter: Rf = 0.8 , Lf = 0.5mH, Cf =80μF
Switching frequency: fp = 5 kHz
Linear Load: L = 40mH, R =10
Nonlinear load : smooth filter ( Rc = 0.02 , Lc = 1mH ), load of DC ( Rd = 5 , Ld = 60mH )
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